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Q & A: What does gravity do to clocks?

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Most recent answer: 09/15/2011
Q:
I'm starting to understand how gravity slows time and how approaching the speed of light also slows time down. What I would like to know is what the natural "speed" of time is? Like if I'm in a space ship, out in open space, with a momentum of zero, and there is no gravity to affect me, at what rate will my clock run? Maybe you can say it runs twice as fast as it does on Earth or whatever the quantitative effect is. Also in a related area, I know some atomic clocks are based on measurements of atoms or isotopes. If an isotope was subjected to more gravity, would its half-life be increased or is the breakdown maintain the same clocklike feature. Thanks. Greg W
- Greg (age 36)
Dubuque, Iowa
A:
The question "at what rate will my clock run?" gets trickier the more you think about it. All your own clocks- your heart rate, your wrist watch, your carbon-14 dating, etc.- run at the same rates with respect to each other as they would anywhere else. In that sense, I guess the answer is "at the usual rate".

The interesting effects come in only when observers look at somebody else's clocks. One meaningful version of your question would be "how fast does somebody on Earth think my clocks run?" That answer depends on two things:
1. Your speed, as measured by somebody on Earth.
2. The pattern of gravitational field between you and the Earth, again as seen by the Earth

I can give a definite answer if we make up some facts for these. You say "zero momentum", I suppose with respect to Earth, so we'll set the speed to zero. That means that there's no Special Relativistic effect on your clock speed, as seen by Earth. 

Let's take the simplest reasonable pattern for the gravitational field here: just the Earth's field by itself. It's uphill from Earth to distant space, and that makes the distant clocks run faster. The net effect is a factor of (1+gR/c2) where g is the gravitational acceleration near the Earth's surface, R is the Earth's radius, and c is the speed of light. That's just a little less than a one part per billion speed-up.  This simple approximation is in fact roughly what goes on with the geosynchronous satellites used in GPS systems, which have to correct for the effect.

With regard to the radioactive isotopes, as I mentioned, their decay rates stay proportional to the rates of all other local clocks.

Mike W.

(published on 09/14/2011)

Follow-Up #1: What does speed do to time?

Q:
People to whom SR is introduced seem to always make the same mistaken assumption : that speed alone slows clocks. Your clock will always run at the same rate to you regardless of your speed or the gravitational influence. It is when you COMPARE your clock to the others' clocks (they weren't in the same reference frame as you) that you notice time dilation. Even if your spaceship move at 99.9999999% of c, the length of a second will remain one second for you, but will last decades for those who are not moving relative to your spaceship. So in the end, there is no such thing as 'the speed of time'. Time always flows normally for everybody who are in the same reference frame, but at different rates for those who AREN'T in the same reference frame. And Einstein demonstrated that there is no such thing as a 'unique reference frame' against which everything is compared to! Now why things behave like this is an unanswerable question ; it is just like that! So for your question, what does gravity do to clocks? For those in that reference frame, gravity does...nothing to clocks except making them fall unto the ground! I too made those same mistaken assumptions when I was 1st introduced to SR.
- PostSRnewbie!
A:
Thanks for the nice vivid description.

Mike W.

(published on 09/15/2011)

Follow-up on this answer.